32 THE MOLECULAR ARCHITECTURE OF PLANT CELL WALLS 



reasons of simplicity of later expression, confined to cellulosic 

 materials alone. 



Crystal lattices 



It is the very essence of a crystal that its molecules shall be arranged 

 in some very regular way, and it is naturally the task of the crystallo- 

 grapher in the first place to define this regularity. The first question is, 

 therefore, how much is needed to be known to achieve this end? Con- 

 sider first a very simple case of a series of points arranged in a straight 

 line, ignoring for the time being the type of atom, or atom group, 

 associated with each point but assuming that each point is identical 

 with any other in this respect. Then if the points are arranged regularly, 

 exactly the same distance apart, this arrangement could be regarded as 

 a "hnear" crystal or a one-dimensional lattice (Fig. lO(fl)). Knowledge, 

 therefore, of a, the distance apart of the points, is all that is needed to 

 define the system completely. One parameter defines the lattice. If, 

 now, a number of such lines of points are placed parallel to each other 

 (Fig. 10(6)), again regularly the same distance apart, and bearing some 

 constant positional arrangement to each other such as that shown in the 

 figure, then three parameters are necessary to define the new, two- 

 dimensional lattice — a, and b, the distances apart of the points along 

 two different directions, and the angle between these two parameters. 

 These define a parallelogram ABEF such that by the regular placing of 

 other identical parallelograms on each side of ABEF, and continuing 

 this process indefinitely throughout the plane, then the whole "crystal" 

 can be built up. Now, however, these are not the only three parameters 

 which could be chosen to define the structure; a parallelogram such as 

 CDFG could be used with exactly the same final result, and there is 

 obviously, in fact, an infinite number of parallelograms which could 

 arbitrarily be chosen. The only reason for preferring ABEF would be 

 its simplicity. 



If, now, sheets of points as in Fig. 10(6) are arranged parallel to each 

 other, one over the other and arranged regularly the same distance apart 

 (Fig. 10(c)), then in general six parameters are needed to define the 

 lattice completely and the labour involved is consequently considerably 

 increased. Fortunately, in the monoclinic crystal class to which cellu- 

 lose belongs, the number is reduced to four, since a=y=90°. Here 

 again it should be noted that though the parameters marked on the 

 figure delineate a parallelepiped ABEFLMOP, regular repetition of 

 which throughout space will reproduce the system, this again is 

 not the only parallelepiped which will satisfy this condition, and 



